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Compound Interest: What It Is and How It Works

Learn about the mathematical principle that can transform your savings.

You’ve likely heard how important it is to start saving early in life. The reasoning behind this? Compound interest.

Compound interest is a mathematical principle where interest accrues not only on the amount you invest—but also on the interest accrued on it. As time goes on and interest keeps accruing, the amount builds far more rapidly than it could without the compounding.

For example, say you invest $1,000 with an interest rate of 8%. At the end of the year, your investment will grow to $1,080—that’s simple interest, which still leaves you with more money than you started with. However, with compound interest, as time goes on, the interest will accumulate on not just the amount you invest (the $1,000)—it will also grow on the interest ($80 for year one).

Here’s a deeper look at the benefits of investing early because of compound interest:

A 25-year-old starts saving $1,000 a year in her retirement account, earning 8% interest annually. She saves $1,000 each year for 10 years. A 35-year-old also starts to save $1,000 in his retirement account, earning 8% interest annually. He saves $1,000 each year for 15 years. Lastly, a 45-year-old starts to save $1,000 in his retirement account, earning 8% interest annually. He saves $1,000 each year for 20 years.

Naturally, you would assume that the 45-year-old ended up with the most in his savings, having contributed $5,000 more than the 35-year-old and $10,000 more than the 25-year-old. However, due to the combination of time and compound interest, the 25-year-old is actually the one who ends up saving the most, even after contributing the least amount total. Why?

Even after the 25-year-old stops contributing $1,000 per year to her retirement account, interest keeps accumulating at a rate each year so that the other two don’t even have a chance to catch up. This is often referred to as a “snowball” effect. Although both the 35- and 45-year-olds saved for longer periods of time, their money has less time to reap the benefits of compound interest and grow. With this, they’re behind before they’ve even started.

Here is the math:

Age

25-year-old's Contribution

25-year-old's Year-End Value

35-year-old's Contribution

35-year-old's Year-End Value

45-year-old's Contribution

45-year-old's Year-End Value

25

$1,000

$1,080.00

26

$1,000

$2,246.40

27

$1,000

$3,506.11

28

$1,000

$4,866.60

29

$1,000

$6,335.93

30

$1,000

$7,922.80

31

$1,000

$9,636.63

32

$1,000

$11,487.56

33

$1,000

$13,486.56

34

$1,000

$15,645.49

35

$16,897.13

$1,000

$1,080.00

36

$18,248.90

$1,000

$2,246.40

37

$19,708.81

$1,000

$3,506.11

38

$21,285.51

$1,000

$4,866.60

39

$22,988.35

$1,000

$6,335.93

40

$24,827.42

$1,000

$7,922.80

41

$26,813.62

$1,000

$9,636.63

42

$28,958.71

$1,000

$11,487.56

43

$31,275.40

$1,000

$13,486.56

44

$33,777.43

$1,000

$15,645.49

45

$36,479.63

$1,000

$17,977.13

$1,000

$1,080.00

46

$39,398.00

$1,000

$20,495.30

$1,000

$2,246.40

47

$42,549.84

$1,000

$23,214.92

$1,000

$3,506.11

48

$45,953.83

$1,000

$26,152.11

$1,000

$4,866.60

49

$49,630.13

$1,000

$29,324.28

$1,000

$6,335.93

50

$53,600.54

$31,670.23

$1,000

$7,922.80

51

$57,888.59

$34,203.84

$1,000

$9,636.63

52

$62,519.67

$36,940.15

$1,000

$11,487.56

53

$67,521.25

$39,895.36

$1,000

$13,486.56

54

$72,922.95

$43,086.99

$1,000

$15,645.49

55

$78,756.78

$46,533.95

$1,000

$17,977.13

56

$85,057.32

$50,256.67

$1,000

$20,495.30

57

$91,861.91

$54,277.20

$1,000

$23,214.92

58

$99,210.86

$58,619.38

$1,000

$26,152.11

59

$107,147.73

$63,308.93

$1,000

$29,324.28

60

$115,719.55

$68,373.64

$1,000

$32,750.23

61

$124,977.12

$73,843.53

$1,000

$36,450.24

62

$134,975.28

$79,751.02

$1,000

$40,446.26

63

$145,773.31

$86,131.10

$1,000

$44,761.96

64

$157,435.17

$93,021.58

$1,000

$49,422.92

65

$170,029.99

$100,463.31

$53,376.76

Total

$10,000

$170,029.99

$15,000

$100,463.31

$20,000

$53,376.76

The highlighted cells indicate the years in which the individual contributed $1,000, with the remaining cells indicating the years in which the investment grew solely due to compound interest. With this, the 25-year-old’s total came to $170,029.99, the 35-year-old’s to $100,463.31 and the 45-year-old’s to $53,376.76. After contributing only half of the amount that the 45-year-old did and in just half the time, the 25-year-old’s savings amounted to approximately $116,653.23 more.

Other considerations

Of course, the amount accumulated from compound interest is based on the compounding period (quarterly, yearly, etc.) and is subject to change based on interest rates. Time is an element that cannot be changed. However, one constant with compound interest is that the earlier you start, the more time your savings will have to grow. This is a concept that is crucial to understanding exactly why it’s so important to start saving for retirement early. While it can be tempting to avoid opting into a defined contribution plan in order to keep more of your money in your pocket, especially early on in your career, it can be extremely difficult to make up for the lost time and will only continue to get more difficult.

To get the most out of your money and to avoid having to work much harder to save a fraction as much as you could have, it’s wise to start saving and preparing for the future as soon as possible.

Interested in discussing this topic further with a financial advisor? With offices in 23 states, there is likely a North Star financial advisor near you. Contact an advisor here.

Written by North Star Resource Group.

This is a hypothetical example for illustrative purposes only and does not indicate the performance of any particular product. These values assume that the currently illustrated non-guaranteed elements will continue unchanged for all years shown. This is not likely to occur and actual results may be more or less favorable than those shown. The example does not take into account the costs associated with investing. Investments will fluctuate and when redeemed may be worth more or less than when originally invested.

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